The Infinite and the Finite

[RicardoSmith23]

Wait, I thought omniscient meant knowing everything. If the universe is not infinite, then omniscient is not either right?

The dilemma is whether omniscience means an "infinite" amount of knowledge, which is what I assumed what it meant, or "all-knowing" in the sense of the ability to know every finite (aka, true) fact. The first is, by definition, impossible. The second is...not really an important topic of conversation at all.

[Persephone]

The second is...not really an important topic of conversation at all.

Again, not the point of this topic, but finite omniscience kind of is important. If an entity, no matter how unlikely, can know every finite fact, then the potential for a form of godhood does exist. You've gotten rid of the monotheist gods, but those annoying all knowing genies are still hangin' in there.

Edited September 24, 2012 by softwareNerd
Quote tag edit

[agrippa1]

I'm confused over the confusion. I haven't advanced a position as to whether there are upper limits on time and space relations, i.e. is it the case that the two furthest particles can be no further apart than X (or no closer together than Y)? I have no reason to believe that there are such size limits on the universe (at the lower end I mean as "fundamental limit", not derived from other facts) but if there were, it would not be horrifying to me.The only sane way to talk about the infinite is as an unbounded measurement, one with no principled limit, but one which always has a definite (finite) value when dealing with an actual instance.

In measurement, instance is to infinite as segment is to line. Therefore, it is meaningless to speak of an instance of the infinite, except as a finite subcomponent of an infinite continuum. Conceptually, instance and infinite are mutually exclusive. The fact that any given instance of measurement in existence is not infinite does not necessarily lead to the conclusion that existence itself is not infinite. Only the definition of the universe as bounded can lead us to conclude that it is not infinite. Similarly, only the premise that only the universal matter (the products of our big bang) that we conceive of composes the universe can lead us to conclude that the amount of matter in the universe is finite. We have a rough idea of the scale (distance, time & matter) of our "universe," but our definition of universe is limited by the event horizon imposed on us by physics. We can choose to define existence as that which lies within the event horizon of our universe, but in doing so, we are simply arbitrarily imposing a finite limit on what still may be an infinite continuum.

[avgleandt]

If the universe was infinite in size and in time then the sky would be just as bright during the night as it is during the day.

Edited May 15, 2008 by avgleandt

[Greebo]

If the universe was infinite in size and in time then the sky would be just as bright during the night as it is during the day.

:confused:

Explain the physics please.

[agrippa1]

If the universe was infinite in size and in time then the sky would be just as bright during the night as it is during the day.

The sky is just as bright during the night as it is during the day.*

*not counting the sun, of course.

[avgleandt]

:confused:

Explain the physics please.

lol. Well imagine your in an infinite forrest. YOu shoot an arrow that allways flys foward, kinda like a beam of light. Eventually that arrow is going to hit a tree. Even if you take the trees, and spread them apart really really far, eventually that arrow would hit a tree. When you look up at the sky, you see stars, but you also see vast dark areas in between the stars. That vast dark areas would not be possible if the universe was infinite. Every part of the sky would be filled with light. Taken that there has also been an infinite amount of time for the light to reach us. Anywhere in the sky you would look there would be a star or a source of light, the whole sky would be as bright as the sun.

[Chops]

If an entity, no matter how unlikely, can know every finite fact, then the potential for a form of godhood does exist.

It's important to remember that "knowing" requires, at it's foundation, perception. No being can know of a supernova 1 million light years away until 1 million years after the fact because nothing travels faster than light, including "knowledge." An omniscient being would need to be able to perceive everything from all angles and perspectives simultaneously, as it happens. The act of being a "receptive" and simply harvesting whatever information arrives (following the laws of physics) would not be an attribute of a god, but of a being (or device) with perceptive capabilities.

That something could conceivably "know" something without perception is the very definition of faith. It's not possible to know the state of every atom and subatomic particle in the universe at any one time. Which would be the fundamental requirement of omniscience.

[DavidOdden]

Anywhere in the sky you would look there would be a star or a source of light, the whole sky would be as bright as the sun.

Problem is, almost all of them would be infinitely far away, thus undetectable.

[EC]

I've already explained and linked to the Objectivist answer to this question. I wasn't just spouting my opinion on the matter. You guy except for David are all going on some irrational tangents that have nothing to do with Objectivism or reality. Please go back and reread the essay I linked to until you understand it. If you have any difficulties, I should be able to answer your questions. But remember I like to give quick, concise answers that don't take a long time to type. You'll tend to find that when something is true it is easy to sum up and doesn't require long pointless discussions debating irrelevant, incorrect, or arbitrary premises.

[Chops]

Problem is, almost all of them would be infinitely far away, thus undetectable.

Or burnt out.

[agrippa1]

I've already explained and linked to the Objectivist answer to this question. I wasn't just spouting my opinion on the matter. You guy except for David are all going on some irrational tangents that have nothing to do with Objectivism or reality. Please go back and reread the essay I linked to until you understand it. If you have any difficulties, I should be able to answer your questions. But remember I like to give quick, concise answers that don't take a long time to type. You'll tend to find that when something is true it is easy to sum up and doesn't require long pointless discussions debating irrelevant, incorrect, or arbitrary premises.

I read it. The argument begins with this assertion:

"Since the infinite is the impossible..."

Which is never addressed.

Later, he quotes Rand:

"Since everything is finite, the universe is finite."

The premises here are:

Every thing is finite.

The universe is a thing.

Therefore:

The universe is finite.

The problem with this syllogism is that "universe" is subsumed under "thing." Therefore, the first premise can only be true if the universe is finite. Since that's the answer being sought, isn't the syllogism begging the question?

[EC]

I read it. The argument begins with this assertion:

"Since the infinite is the impossible..."

Which is never addressed.

Later, he quotes Rand:

The premises here are:

Every thing is finite.

The universe is a thing.

Therefore:

The universe is finite.

The problem with this syllogism is that "universe" is subsumed under "thing." Therefore, the first premise can only be true if the universe is finite. Since that's the answer being sought, isn't the syllogism begging the question?

No because saying every"thing" is finite is simply a restatement of the Law of Identity, ever thing possesses a finite identity, including the universe itself. The Law of Identity is a basic axiom on which all new knowledge is based.

[EC]

I protest against the use of infinite magnitude as something completed, which in mathematics is never permissible. Infinity is merely a facon de parler, the real meaning being a limit which certain ratios approach indefinitely near, while others are permitted to increase without retriction.--Carl Friedrich Gauss

[y_feldblum]

The universe is not a "thing."

[Greebo]

The universe is not a "thing."

It isn't?

How does it exist then?

[DavidOdden]

It isn't?

How does it exist then?

It's everything. Everything isn't a thing.

[agrippa1]

No because saying every"thing" is finite is simply a restatement of the Law of Identity, ever thing possesses a finite identity, including the universe itself. The Law of Identity is a basic axiom on which all new knowledge is based.

But the universe has no context within which to make the assertion that it is of the same class as any other "thing." Finite, measured against what scale? Saying that the universe is a thing, in the sense that everything subsumed by the universe is a thing, seems to be, if not a contradiction, then at least questionable.

The universe does not exist within itself. It is apart, conceptually from every other "thing" "in" the universe. Therefore assertions made about every "thing" in the universe do not necessarily apply to the universe itself.

For instance, every thing is created in a process. Are we to presume that the universe was created? Every thing has position, scale, time, when measured against other things within the context of the universe - how can we say the same about the universe, with nothing larger to measure it against. The universe is, by definition, larger than any thing, distance, scale, etc., that we could give an instance of (unless it has a closed topology). Isn't that the definition of "infinite?"

edit: that's not to argue that the universe is necessarily infinite, only that we can't say one way or the other, given our current state of knowledge.

Edited May 16, 2008 by agrippa1

[DavidOdden]

that's not to argue that the universe is necessarily infinite, only that we can't say one way or the other, given our current state of knowledge.

Given our current state of knowledge, what is an example of some actual infinity? If there are no actual infinities, then that is sufficient reason to decide that the universe if finite. There are vast numbers of things that are finite, so we can't seriously doubt that a possible answer is "finite". Is there a shred of even conceptual support for an anctually infinite universe? If not, why would one accept an arbitrary claim to the effect that -- exceptionally -- the universe is actually infinite?

[agrippa1]

Given our current state of knowledge, what is an example of some actual infinity? If there are no actual infinities, then that is sufficient reason to decide that the universe if finite. There are vast numbers of things that are finite, so we can't seriously doubt that a possible answer is "finite". Is there a shred of even conceptual support for an anctually infinite universe? If not, why would one accept an arbitrary claim to the effect that -- exceptionally -- the universe is actually infinite?

What you really say here is "If there are no actual infinities, aside from the universe, then that is sufficient reason to decide that the universe is finite." Again, the question is begged, by assuming that the universe shares an attribute with every one of its subsumed components.

Any example we might give of an actual infinity would lie within the universe and would therefore necessitate that the universe be infinite. Since we can provide no examples of infinity within the universe, all we can say for sure is that the universe is larger than anything which could exist within it. Included in the set of possibilities which meet that requirement is an infinite universe.

So we can't prove that the universe is finite simply by pointing to the things within it which are.

On the other hand, I might ask you if you can point to a thing which is not smaller than any other thing. In the absence of such an actual entity, and given the premise that the universe is not smaller than any other thing, can you come to any other conclusion than that the finiteness of the universe is not comparable to the finiteness of any thing within it? Given that we can establish that the finiteness of the universe is disconnected, conceptually, from the finiteness of the things which is subsumes, there results that there is no evidence that the universe is in fact finite, and at least conceptual evidence that universe is potentially infinite.

Further, given the concept of "finite," (measurable, countable, subject to limitations) which implies a limit, there is implicit in the concept of a finite universe the conclusion that something (be it an empty void, or...) lies beyond the finite limits of universe. This is a contradiction of the concept "universe" and provides at least a shred of conceptual evidence that the universe is necessarily (not just possibly) infinite.

[DavidOdden]

What you really say here is "If there are no actual infinities, aside from the universe,

Where exactly did I really say that? I can't find it in my copy. I say "if there are no actual infinities". Period. If you have some evidence that there is such a thing as an "actual infinity", then we can discuss applying that to the universe. Otherwise, you're just making stuff up. If you think that the totality of existence has a special property that sets it apart from any part of the universe, you can shoulder your burden of proof. I needn't show anything, since I'm simply saying that the totality of existence is not radically different from any subpart of it.

So we can't prove that the universe is finite simply by pointing to the things within it which are.

And you can't prove that the universe is infinite by pointing to the impossibility of proving that the universe isn't the unique actual infinity.

[y_feldblum]

To speak of a thing is to speak of some bounded aspect of reality, mentally separated from the rest of reality. The universe, being everything, is not a thing.

One ought not to confuse the universe with an actual infinity. The universe is not a thing. If it is indeed possible to go on indefinitely observing new things, it is still problematic to speak of the universe as an actual infinity. Nothing is an actual infinity: i.e., no thing is an actual infinity: i.e., no bounded aspect of reality, mentally separated from the unbounded rest of reality, is itself unbounded.

The universe does not "contain" the things in the universe. The universe is the things in the universe. It is everything. Note that space and time are not things, but properties of things or relationships between things - properties such as location, extent, duration, motion, etc. It is impossible to observe space and time "in themselves" - we observe the above listed properties which things tend to possess. Space and time are unbounded, in the sense that a thing can be anywhere or anywhen, can have any extent or any duration. An unbounded space and time does not make for an "infinite universe," however. The universe is everything - not every potential location or potential time of things.

[Nyronus]

I protest against the use of infinite magnitude as something completed, which in mathematics is never permissible. Infinity is merely a facon de parler, the real meaning being a limit which certain ratios approach indefinitely near, while others are permitted to increase without retriction.--Carl Friedrich Gauss

So it seems that what your objecting to is a the semantic use of the word infinity, not the idea that the universe is boundless or such. Am I making a mistake in that assessment?

[Greebo]

I submit for consideration that the word "The Universe" and the word "Existence" are not interchangeable or synonymous.

Existence is all that exists, ever did, ever will.

We have scientific evidence that this universe, our current one, did not always exist as it is now. It was created from a singularity. Presumably, prior to that was another universe, in an endless cycle.

Existence, however, consists of every universe that ever has existed, ever will exist, and if alternate universes exist as have been theorized, existence includes them as well.

Therefore, the universe *is* a thing.

[DavidOdden]

We have scientific evidence that this universe, our current one, did not always exist as it is now. It was created from a singularity. Presumably, prior to that was another universe, in an endless cycle.

What is your evidence that there was another universe prior to the big bang; what indeed is your evidence that scientists hold that before the big bang there was another universe?